Author Archives: Fredrik

In the implementation of ball arithmetic I wrote about previously, arithmetic is done naively using FLINT (fmpz) integers. This is easy to implement but adds quite a lot of overhead at low precision (up to a precision of several hundred … Continue reading →

In the last post, I discussed computing the exponential function. With that being implemented, it’s not much work to do logarithms as well. If we can evaluate the exponential function, then we can compute $y = \log x$ by using … Continue reading →

The overwhelming majority of the time when I use arbitrary-precision arithmetic, I only need precision slightly higher than hardware precision; typically 30-40 digits, occasionally perhaps 100 digits, and only very rarely 1000 digits or more. About two years ago, I … Continue reading →

In my last post, I mentioned using binary splitting to compute $\zeta(n)$ to extremely high precision for small $n$. I have now added a function to Arb for evaluating $\zeta(n)$ that selects between several different algorithms depending on both $n$ … Continue reading →